Quantum field theory can be understood through gauge theories. It is already established that the gauge theories can be studied either perturbatively or non-perturbatively. Perturbative means using Feynman diagrams an...Quantum field theory can be understood through gauge theories. It is already established that the gauge theories can be studied either perturbatively or non-perturbatively. Perturbative means using Feynman diagrams and non-perturbative means using Path-integral method. Operator regularization (OR) is one of the exceptional methods to study gauge theories because of its two-fold prescriptions. That means in OR two types of prescriptions have been introduced, which gives us the opportunity to check the result in self consistent way. In an earlier paper, we have evaluated basic QED loop diagrams in (3 + 1) dimensions using the both methods of OR and Dimensional regularization (DR). Then all three results have been compared. It is seen that the finite part of the result is almost same. In this paper, we are interested to evaluate the same basic loop diagrams in (2 + 1) space-time dimensions, because of two reasons: the main reason in (2 + 1) space-time dimensions, these loops diagrams are finite, on other hand, there are divergences in (3 + 1) space-time dimensions and the other reason is to see validity of using OR to evaluate Feynman loop diagrams in all dimensions. Here we have used both prescriptions of OR and DR to evaluate the basic loop diagrams and compared the results. Interestingly the results are almost same in all cases.展开更多
By applying the path-integral formulation and the Feynman theorem, we calculate the off-diagonal superconducting correlation in an ultrasmall metallic grain. Unlike its behavior in the bulk limit, we find that this co...By applying the path-integral formulation and the Feynman theorem, we calculate the off-diagonal superconducting correlation in an ultrasmall metallic grain. Unlike its behavior in the bulk limit, we find that this correlation function is an intensive quantity in this case. Therefore, superconductivity is indeed completely suppressed by quantum fluctuations as the diameter of the grain shrinks to the nanometer scale. This conclusion confirms the previous results by numerical calculations. Furthermore, it also imposes a strong constraint on the delocalizing amplitude of the pair-mixing function, which was recently proposed to characterize superconductivity in the canonical ensemble.PACS numbers: 74.20.Fg, 73.23.Hk, 74.80.展开更多
常规非线性反演方法虽然对初始模型的依赖大为减弱,但局部收敛现象和计算速度慢仍然是瓶颈.本文提出了一种新的反演方法——量子路径积分算法(Quantum Path Integral Algorithm,简称QPIA).该方法引入量子力学的横向场、传播子等概念,并...常规非线性反演方法虽然对初始模型的依赖大为减弱,但局部收敛现象和计算速度慢仍然是瓶颈.本文提出了一种新的反演方法——量子路径积分算法(Quantum Path Integral Algorithm,简称QPIA).该方法引入量子力学的横向场、传播子等概念,并充分利用量子隧穿效应,大大提高反演的效率,具体是通过对反演目标函数的构建,并以Feynman的传播子来构成模型的接收概率来实现.在对一维大地电磁模型和实际数据进行试验后,表明该方法比常规反演方法更能够精确、稳定和快速地逼近真实模型.展开更多
The response statistics of a compliant offshore structure excited by slowly varying wave drift forces is calculated by use of a numerical path integral solution method. The path integral solution is based on the Ganss...The response statistics of a compliant offshore structure excited by slowly varying wave drift forces is calculated by use of a numerical path integral solution method. The path integral solution is based on the Ganss-Legendre interpolation scheme, and the values of the response probability density are obtained at the Gauss quadrature points in sub-intervals. It is demonstrated that a distinct advantage of the path integral solution is that the joint probability density of the response displacement and velocity is one of the by products of the calculations. This makes it possible to calculate the mean level up-crossing rates, which provides estimates of the exceedance probabilities of specified response levels for given time periods.展开更多
为使交互式水域环卫机器人(Interactive Water Sanitation Vehicle,IWSV)在进行垃圾收集时成功捕获水中浮动垃圾并顺利规避水域障碍物,提出一种将基于采样的快速搜索随机树(Rapidly-exploring Random Tree,RRT)算法与速度障碍模型相结...为使交互式水域环卫机器人(Interactive Water Sanitation Vehicle,IWSV)在进行垃圾收集时成功捕获水中浮动垃圾并顺利规避水域障碍物,提出一种将基于采样的快速搜索随机树(Rapidly-exploring Random Tree,RRT)算法与速度障碍模型相结合的路径规划算法。利用双目摄像头基于视差定位法获取水域动态障碍物的位置坐标,利用IWSV搭载的感应元件获取其自身与障碍物的相对方位角,基于速度障碍法计算可成功避开障碍物的移动角度调整范围,对更优的RRT算法中的随机采样过程进行进一步优化,得到改进的避障路径规划算法。考虑实际应用场景,引入抗积分饱和比例积分微分控制(Proportional Integral Differentiational Control,PID Control)法使航向控制器的控制效果更为精准有效。在实景测试时避障路径规划算法存在稳健性,基于到达时间(Time of Arrival,TOA)定位法进行仿真分析。仿真试验结果表明,该路径规划算法比RRT算法和改进前的RRT算法路径规划效果更优,可靠性更好,可在较短时间内避障并得到较优移动路径。在实景测试时基于TOA的Chan算法更加符合定位估计需求,且IWSV本体感应装置的噪声测算宜在10 m以内。展开更多
This paper presents an elasto-viscoplastic consistent tangent operator (CTO) based boundary element formulation, and application for calculation of path-domain independentJ integrals (extension of the classicalJ integ...This paper presents an elasto-viscoplastic consistent tangent operator (CTO) based boundary element formulation, and application for calculation of path-domain independentJ integrals (extension of the classicalJ integrals) in nonlinear crack analysis. When viscoplastic deformation happens, the effective stresses around the crack tip in the nonlinear region is allowed to exceed the loading surface, and the pure plastic theory is not suitable for this situation. The concept of consistency employed in the solution of increment viscoplastic problem, plays a crucial role in preserving the quadratic rate asymptotic convergence of iteractive schemes based on Newton's method. Therefore, this paper investigates the viscoplastic crack problem, and presents an implicit viscoplastic algorithm using the CTO concept in a boundary element framework for path-domain independentJ integrals. Applications are presented with two numerical examples for viscoplastic crack problems andJ integrals.展开更多
The path integral Monte Carlo(PIMC) method is employed to study the thermal properties of C70 with one, two,and three H2 molecules confined in the cage, respectively. The interaction energies and vibrationally average...The path integral Monte Carlo(PIMC) method is employed to study the thermal properties of C70 with one, two,and three H2 molecules confined in the cage, respectively. The interaction energies and vibrationally averaged spatial distributions under different temperatures are calculated to evaluate the stabilities of(H2)n@C70(n = 1, 2, 3). The results show that(H2)2@C70is more stable than H2@C70. The interaction energy slowly changes in a large temperature range,so temperature has little effect on the stability of the system. For H2@C70and(H2)2@C70, the interaction energies keep negative; however, when three H2 molecules are in the cage, the interaction energy rapidly increases to a positive value.This implies that at most two H2 molecules can be trapped by C70. With an increase of temperature, the peak of the spatial distribution gradually shifts away from the center of the cage, but the maximum distance from the center of H2 molecule to the cage center is much smaller than the average radius of C70.展开更多
文摘Quantum field theory can be understood through gauge theories. It is already established that the gauge theories can be studied either perturbatively or non-perturbatively. Perturbative means using Feynman diagrams and non-perturbative means using Path-integral method. Operator regularization (OR) is one of the exceptional methods to study gauge theories because of its two-fold prescriptions. That means in OR two types of prescriptions have been introduced, which gives us the opportunity to check the result in self consistent way. In an earlier paper, we have evaluated basic QED loop diagrams in (3 + 1) dimensions using the both methods of OR and Dimensional regularization (DR). Then all three results have been compared. It is seen that the finite part of the result is almost same. In this paper, we are interested to evaluate the same basic loop diagrams in (2 + 1) space-time dimensions, because of two reasons: the main reason in (2 + 1) space-time dimensions, these loops diagrams are finite, on other hand, there are divergences in (3 + 1) space-time dimensions and the other reason is to see validity of using OR to evaluate Feynman loop diagrams in all dimensions. Here we have used both prescriptions of OR and DR to evaluate the basic loop diagrams and compared the results. Interestingly the results are almost same in all cases.
文摘By applying the path-integral formulation and the Feynman theorem, we calculate the off-diagonal superconducting correlation in an ultrasmall metallic grain. Unlike its behavior in the bulk limit, we find that this correlation function is an intensive quantity in this case. Therefore, superconductivity is indeed completely suppressed by quantum fluctuations as the diameter of the grain shrinks to the nanometer scale. This conclusion confirms the previous results by numerical calculations. Furthermore, it also imposes a strong constraint on the delocalizing amplitude of the pair-mixing function, which was recently proposed to characterize superconductivity in the canonical ensemble.PACS numbers: 74.20.Fg, 73.23.Hk, 74.80.
文摘常规非线性反演方法虽然对初始模型的依赖大为减弱,但局部收敛现象和计算速度慢仍然是瓶颈.本文提出了一种新的反演方法——量子路径积分算法(Quantum Path Integral Algorithm,简称QPIA).该方法引入量子力学的横向场、传播子等概念,并充分利用量子隧穿效应,大大提高反演的效率,具体是通过对反演目标函数的构建,并以Feynman的传播子来构成模型的接收概率来实现.在对一维大地电磁模型和实际数据进行试验后,表明该方法比常规反演方法更能够精确、稳定和快速地逼近真实模型.
文摘The response statistics of a compliant offshore structure excited by slowly varying wave drift forces is calculated by use of a numerical path integral solution method. The path integral solution is based on the Ganss-Legendre interpolation scheme, and the values of the response probability density are obtained at the Gauss quadrature points in sub-intervals. It is demonstrated that a distinct advantage of the path integral solution is that the joint probability density of the response displacement and velocity is one of the by products of the calculations. This makes it possible to calculate the mean level up-crossing rates, which provides estimates of the exceedance probabilities of specified response levels for given time periods.
文摘为使交互式水域环卫机器人(Interactive Water Sanitation Vehicle,IWSV)在进行垃圾收集时成功捕获水中浮动垃圾并顺利规避水域障碍物,提出一种将基于采样的快速搜索随机树(Rapidly-exploring Random Tree,RRT)算法与速度障碍模型相结合的路径规划算法。利用双目摄像头基于视差定位法获取水域动态障碍物的位置坐标,利用IWSV搭载的感应元件获取其自身与障碍物的相对方位角,基于速度障碍法计算可成功避开障碍物的移动角度调整范围,对更优的RRT算法中的随机采样过程进行进一步优化,得到改进的避障路径规划算法。考虑实际应用场景,引入抗积分饱和比例积分微分控制(Proportional Integral Differentiational Control,PID Control)法使航向控制器的控制效果更为精准有效。在实景测试时避障路径规划算法存在稳健性,基于到达时间(Time of Arrival,TOA)定位法进行仿真分析。仿真试验结果表明,该路径规划算法比RRT算法和改进前的RRT算法路径规划效果更优,可靠性更好,可在较短时间内避障并得到较优移动路径。在实景测试时基于TOA的Chan算法更加符合定位估计需求,且IWSV本体感应装置的噪声测算宜在10 m以内。
基金The project supported by National Natural Science Foundation of China(9713008)Zhejiang Natural Science Foundation Special Funds No. RC.9601
文摘This paper presents an elasto-viscoplastic consistent tangent operator (CTO) based boundary element formulation, and application for calculation of path-domain independentJ integrals (extension of the classicalJ integrals) in nonlinear crack analysis. When viscoplastic deformation happens, the effective stresses around the crack tip in the nonlinear region is allowed to exceed the loading surface, and the pure plastic theory is not suitable for this situation. The concept of consistency employed in the solution of increment viscoplastic problem, plays a crucial role in preserving the quadratic rate asymptotic convergence of iteractive schemes based on Newton's method. Therefore, this paper investigates the viscoplastic crack problem, and presents an implicit viscoplastic algorithm using the CTO concept in a boundary element framework for path-domain independentJ integrals. Applications are presented with two numerical examples for viscoplastic crack problems andJ integrals.
基金supported by the National Natural Science Foundation of China(Grant Nos.11474207 and 11374217)
文摘The path integral Monte Carlo(PIMC) method is employed to study the thermal properties of C70 with one, two,and three H2 molecules confined in the cage, respectively. The interaction energies and vibrationally averaged spatial distributions under different temperatures are calculated to evaluate the stabilities of(H2)n@C70(n = 1, 2, 3). The results show that(H2)2@C70is more stable than H2@C70. The interaction energy slowly changes in a large temperature range,so temperature has little effect on the stability of the system. For H2@C70and(H2)2@C70, the interaction energies keep negative; however, when three H2 molecules are in the cage, the interaction energy rapidly increases to a positive value.This implies that at most two H2 molecules can be trapped by C70. With an increase of temperature, the peak of the spatial distribution gradually shifts away from the center of the cage, but the maximum distance from the center of H2 molecule to the cage center is much smaller than the average radius of C70.
